The present invention relates to a bit error correcting method employing state transitions in a digital VTR or digital optical disk apparatus and particularly to a playback data detecting method for improving bit error rate for random error.
Generally, in a digital VTR and digital optical disk storage device, the discrimination of digital playback data is carried out by assigning a value of "1" when a playback voltage level exceeds a prescribed threshold voltage and assigning a value of "0" when the playback voltage level does not exceed the prescribed threshold level.
In a digital optical disk apparatus, a detecting method known as a partial response (1, 1)+Viterbi decoding method is employed. As shown in FIG. 1, in the digital optical disk apparatus based on the partial response (1, 1)+Viterbi decoding method, an input signal a(t) shown in FIG. 2(a) is converted to a recording signal b(t) shown in FIG. 2(b) in a pre-coder 10 provided on the recording side. Here, the input signal a(t) is an NRZ (non return to zero recording) signal and the recording signal b(t) is an NRZI (non return to zero inverted recording) signal. The recording signal b(t) is recorded on a tape 11. A playback signal c(t) played back from the tape 11, as shown in FIG. 2(c), consists of positive pulses indicating the leading edges of the recording signal b(t) and negative pulses indicating the trailing edges of the recording signal b(t). After noise is added to the playback signal c(t), it is inputted to a partial response (1, 1) equalizer 12. In the partial response (1, 1) equalizer 12, the detection of the playback data is carried out using the correlations between the encoded data of the playback signal c(t) which is digital playback data. In other words, the partial response (1, 1) equalizer 12 is a conventional device for converting the binary playback signal c(t) to a three-value playback equalized output signal d(t) using a conventional partial response (1, 1) encoding method (also known as a duo-binary encoding method). The playback equalized output signal d(t), after being converted to a signal e(t) shown in FIG. 2(d) by passing through a high-pass filter 13, is inputted to a Viterbi decoder 14.
As shown in FIGS. 3 and 4, the Viterbi decoder 14, taking the playback states as state S0 and state S1, makes a transition to state S0 when the signal e(t) of "-1" is inputted during state S0 and makes the value of the output signal f(t) "0." When the signal e(t) of "0" is inputted during state S0, it makes a transition to state S1 and makes the value of the output signal f(t) a value "1." When the signal e(t) of "1" is inputted during state S1, it makes a transition to state S1 and makes the value of the output signal f(t) "0." When the signal e(t) of "0" is inputted during state S1, it makes a transition to state S0 and makes the value of the output signal f(t) "1." When the signal e(t) violating the above-described state transition rules is inputted, bit error correction is performed by detecting an incorrect state and judging an original state. As a result, the error rate for random errors is improved.
When playing back the signal e(t) of "1" in state S1, the probability P.sub.11 of detecting a tiny offset .DELTA.y can be expressed: EQU P.sub.11 =.DELTA.y/{(2.pi.).sup.1/2 .sigma.}.times.exp{-y.sub.k.sup.2 /(2.sigma..sup.2)}
When playing back the signal e(t) of "0" in State S1, the probability P.sub.10 of detecting a tiny offset .DELTA.y can be expressed: EQU P.sub.10 =.DELTA.y/{(2.pi.).sup.1/2 }.times.exp{-(y.sub.k -1).sup.2 /(2.sigma.2)}
When playing back the signal e(t) of "1" in State S0, the probability P.sub.01 of detecting a tiny offset .DELTA.y can be expressed: EQU P.sub.01 =.DELTA.y/{(2.pi.).sup.1/2 .sigma.}.times.exp{-y.sub.k.sup.2 /(2.sigma..sup.2)}
When playing back the signal e(t) of "0" in State S0, the probability P.sub.00 of detecting a tiny offset .DELTA.y can be expressed: EQU P.sub.00 =.DELTA.y/{(2.pi.).sup.1/2 }.times.exp{-(y.sub.k +1).sup.2 /(2.sigma..sup.2)}
Because the length of the metric can be indicated by the logarithm of the negative value of the probabilities, the product of the probability can be expressed as the sum of the logarithm of the negative value of the probability (in other words, the sum of the lengths of the metrics). ##EQU1## -log.sub.e (P.sub.10)=(y.sub.k -1).sup.2 /(2.sigma..sup.2)-log.sub.e .DELTA.y/{(2.pi.).sup.1/2 .sigma.}!
-log.sub.e (P.sub.00)=(y.sub.k +1).sup.2 /(2.sigma..sup.2)-log.sub.e .DELTA.y/{(2.pi.).sup.1/2 .sigma.}! PA1 1.sub.00 = 2.sigma..sup.2 {-log.sub.e (P.sub.00)+log.sub.e (.DELTA.y/((2.pi.).sup.1/2 .sigma.))}-y.sub.k.sup.2 !/2 PA1 1.sub.11 =1.sub.01 =0 PA1 1.sub.10 =y.sub.k +0.5 PA1 1.sub.00 =y.sub.k +0.5 PA1 when m(S1)-m(S0).gtoreq.y+0.5, PA1 m(S1)=m(S0) and PA1 m(S0)=m(S0)+y+0.5: PA1 when y-0.5&lt;m(S1)-m(S0)&lt;y+0.5, PA1 m(S1)=m(S0) and PA1 m(S0)=m(S1): PA1 when m(S1)-m(S0 &lt;y-0.5, PA1 m(S1)=m(S0)-y+0.5 and PA1 m(S0)=m(S1).
The metric will hereinafter be dealt with not as an absolute value but a relative value of length, and the standardized metrics 1.sub.00, 1.sub.01, 1.sub.10, 1.sub.11 are defined as shown in the following formulas: ##EQU2## 1.sub.10 = 2.sigma..sup.2 {-log.sub.e (p.sub.10)+log.sub.e (.DELTA.y/((2.pi.).sup.1/2 .sigma.))}-y.sub.k.sup.2 !/2
and as a result:
Here, if a sample value of the playback signal at time n is y.sub.n and the state metrics of state S1 and state S0 at time n are m.sub.n (S1) and m.sub.n (S0), respectively, then: ##EQU3##
At this time, merge 0, merge 1, and merge 2 are defined as follows: ##EQU4## and the trellis diagram is as shown in FIG. 6: ##EQU5## and the trellis line figure is as shown in FIG. 7: ##EQU6## and the trellis line figure is as shown in FIG. 8.
When the playback data is "y" (-1.ltoreq.y.ltoreq.1), "y+0.5" and "-y+0.5" are calculated from the playback data and merges are judged as follows:
(1) merge 0
(2) merge 1
(3) merge 2
The path is then merged and the most apparently definite path is judged beginning from the point in time of merging the path and progressing towards the past. In the field of communications engineering, this method of path determination is known as the "Viterbi decoding method." Here, in merge 1, even if the path configuration is sought at time n, because the path is not merged at the point of time preceding, the path is not merged at that point in time and the value of the output signal cannot be obtained. However, when merge 0 or merge 2 are generated, the path is merged and the corresponding output signal can be obtained. FIG. 9 is a diagram showing one series of path merging for two states of Viterbi decoding. When the path is merged in this series, the value of the output signal is made "0" for a transition from state S0 to state S0 and a transition from state S1 to state S1, and the value of the output signal is made "1" for a transition from state S0 to state S1 and a transition from state S1 to state S0, and in this manner, the output signal is produced.
This type of conventional, generally-used bit-by-bit determination gives rise to the special characteristics of digital recording and has the advantages of straightforward logic and simple circuitry. Nevertheless, when errors occur in which the threshold in the playback voltage is barely exceeded, bit errors are generated. In addition, once an error has occurred, it is corrected in an error-correcting circuit block, and it not possible to correct it in a discrimination playback circuit block. Further, a partial response (1, 1) detection+two-state Viterbi decoding method that uses the relation of the encoding interval of the playback signal carries out correction of bit errors by using relations based on the three values of the playback signal. Accordingly, in an encoding conversion method that records by converting data bits to channel bits while constraining the number of continuous non-inverse bits within a range of a minimum of "2," an improvement in error rate is achieved by bit error correction when comparing the determination bit by bit, but because this method does not take advantage of the correlation that is generated by constraining the number of continuous non-inverse bits within a range of a minimum of "2," it cannot be said that the potential of the originally recorded codes is being fully used, and there is consequently room for further improvement of the bit error rate. The term "non-inverse bits" as used in the specification and claims means any sequence of bits in which the bits do not change. For example, with regard to "0011100011", inverse bits means "--01--" or "-10--" and non-inverse bits means "--00--" or "--11--". Non-inverse bits within a range of a minimum of 2 means to continue the same bit ("0" or "1") within a range of a minimum of 2.